Quiz 3

Question 1

Cauchy sequence

Answer 1

A sequence that If for every ε>0, there exists an N∈N such that whenever m,n ≥ N it follows that |an - am| < ε

Question 2

sequence of partial sums

Answer 2

sm = b1 + b2 + b3 + … + bm

Question 3

Convergence of a series

Answer 3

Let (bn) be a sequence. The series Σbn converges to B if the sequence (sm) converges to B where sm = b1 +b2 + b3 + ….

Question 4

Monotone Convergence Theorem

Answer 4

If a sequence is monotone and bounded, then it converges

Question 5

Bolzano-Weierstrass Theorem

Answer 5

Every bounded sequence contains a convergent subsequence

Question 6

The Cauchy Criterion

Answer 6

A sequence converges iff it is a Cauchy sequence